You must send your email from the address from which you wish to subscribe or unsubscribe. For instance, to change the address to which announcements are sent,

First unsubscribe with an email sent from your old address and
then subscribe with an email sent from your new address

When using the subscribe or unsubscribe feature, the subject line and message content of your email can be left blank.

IMPORTANT DETAIL: A confirmation email will be sent to you by Google Groups when you subscribe or unsubscribe. This is done to ensure that someone else cannot change your subscription without your awareness. Confirmations are emailed to the addresses(es) from which you sent your subscription request. Unsubscribe and subscribe requests are not activated until you reply to the confirmation email. Depending on your email client, this confirmation might end up in your "junk" folder. Look in that folder if it appears the confirmation email was not received. Confirmation emails usually are received immediately but in some situations may be delayed up to 10 minutes.